tailieunhanh - báo cáo hóa học: " An initial-boundary value problem for the one-dimensional non-classical heat equation in a slab"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: An initial-boundary value problem for the one-dimensional non-classical heat equation in a slab | Salva et al. Boundary Value Problems 2011 2011 4 0 Boundary Value Problems http content 2011 1 4 a SpringerOpen Journal RESEARCH Open Access An initial-boundary value problem for the one-dimensional non-classical heat equation in a slab Natalia Nieves Salva1 2 Domingo Alberto Tarzia1 3 and Luis Tadeo Villa1 4 Correspondence DTarzia@austral. 1CONICET Rosario Argentina Full list of author information is available at the end of the article Abstract Nonlinear problems for the one-dimensional heat equation in a bounded and homogeneous medium with temperature data on the boundaries x 0 and x 1 and a uniform spatial heat source depending on the heat flux or the temperature on the boundary x 0 are studied. Existence and uniqueness for the solution to non-classical heat conduction problems under suitable assumptions on the data are obtained. Comparisons results and asymptotic behavior for the solution for particular choices of the heat source initial and boundary data are also obtained. A generalization for non-classical moving boundary problems for the heat equation is also given. 2000 AMS Subject Classification 35C15 35K55 45D05 80A20 35R35. Keywords Non-classical heat equation Nonlinear heat conduction problems Volterra integral equations Moving boundary problems Uniform heat source 1. Introduction In this article we will consider initial and boundary value problems IBVP for the one-dimensional non-classical heat equation motivated by some phenomena regarding the design of thermal regulation devices that provides a heater or cooler effect 1-6 . In Section 2 we study the following IBVP Problem P1 Ut - Uxx -F Ux 0 t t 0 x 1 t 0 u 0 t f t t 0 P1 u 1 t g t t 0 u x 0 h x 0 x 1 where the unknown function u u x t denotes the temperature profile for an homogeneous medium occupying the spatial region 0 x 1 the boundary data f and g are real functions defined on R the initial temperature h x is a real function defined on 0 1 and